Unformatted text preview: (Remark: Dirac algebra is commonly used in the real world, and, as a course objective, I hope the knowledge you learn in this course can really help your future career in the real world! This preview is a simple exercise to prepare us for using the Dirac algebra to solve quantum SHO—the most important quantum system.) Dirac’s approach in solving quantum SHO is based on commutator relations. Please prove by commutator algebra the following commutator relations: (Hint: a , a + ) , and H are defined in Eq. (6.57), (6.58), (6.62), respectively. You may find the following commutator algebra formula helpful: [x, p]=i ħ...
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 Winter '07
 Lin
 Quantum Chemistry, Hilbert space, Dirac equation, Dirac algebra, following commutator relations

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